Place 1/3 cup chocolate chips and 2 tablespoons milk in a bowl and Microwave 30 seconds and stir until smooth. If necessary, microwave an additional 15 seconds at a time, stirring after each heating, until chips are melted and mixture is smooth when stirred. Spread on bottom of crust. Refrigerate while preparing next step.
Combine marshmallows, remaining 2/3 cup chocolate chips and 1/4 cup milk in small saucepan. Stir constantly over medium heat, until marshmallows are melted and mixture is well blended. Scrape into large bowl and let cool completely.
Stir 2 cups whipped topping into cooled chocolate mixture. Spread 2 cups of the mixture over the chocolate in crust.
Blend remaining whipped topping and remaining chocolate mixture and spread over surface of pie.